"We have received assurances from the Iranians that our sailors are safe and that they will be allowed to continue their journey promptly," White House spokesman Josh Earnest told CNN.
Two U.S. officials told Reuters that it was unlikely the sailors would be released overnight.
While both sides appeared eager not to let the incident escalate further, it came at a delicate time for U.S.-Iranian relations.
Iran and six world powers forged a landmark nuclear accord last July. Formal implementation of the accord could begin in days following steps Iran agreed to take to curb its nuclear activities.
News of the incident broke as U.S. President Barack Obama prepared to make his final State of the Union address to the U.S. Congress. Obama, a Democrat, made the Iran accord a centerpiece of his foreign policy, and Republicans vying to succeed him have assailed him over the deal. Americans elect a new president on Nov. 8.
Iran's semi-official Fars news agency said: "The Revolutionary Guards naval forces seized the American boats two kilometers inside Iranian territorial waters while they were snooping around."
Officials from Iran and the United States are negotiating to free the crew, Fars reported. U.S. defense officials said nine men and one woman were aboard the two vessels seized.
A senior U.S. defense official said the United States had lost contact earlier in the day with two small craft en route from Kuwait to Bahrain.
Another U.S. official said mechanical issues may have disabled one of the boats, leading to a situation in which both ships drifted inadvertently into Iranian waters.
Iranian Foreign Minister Mohammad Javad Zarif assured U.S. Secretary of State John Kerry that the U.S. sailors would be allowed to continue their journey promptly, another U.S. official said.
SAILORS SAID TO BE SAFE
In a statement, Iran's Islamic Revolutionary Guard Corps confirmed it seized the boats and said the sailors were safe and well. It said France's Charles de Gaulle aircraft carrier was near the seized U.S. boats.
They were on board two riverine patrol boats, one of the officials said. Riverine boats are 38-foot long, high-speed patrol boats used by the U.S. Navy and Marines to patrol rivers and littoral waters.
It was the latest reported incident between U.S. and Iranian forces in the Gulf in recent weeks.
The U.S. Navy said late last month that an Iranian Revolutionary Guards vessel fired unguided rockets on Dec. 26 near warships including the aircraft carrier USS Harry S Truman in the Strait of Hormuz. Iran denied the vessel had done so.
Previous Iranian seizures involved British sailors and marines.
In June 2004, Iran arrested six Royal Marines and two naval personnel - part of a U.S.-led force in Iraq - for straying into its waters, stirring diplomatic tensions between the two. Following negotiations the eight were freed three days later.
In March 2007, Iranian forces seized 15 British servicemen - eight Royal Navy sailors and seven marines - in the mouth of the Shatt al-Arab waterway that separates Iran and Iraq, triggering a diplomatic crisis at a time of heightened tensions over Tehran's nuclear ambitions. They were held for 13 days.
In November 2009, Iranian naval vessels detained five Britons on a racing yacht en route from Bahrain to Dubai. They were released a week later.
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